Nonmonotone projected Barzilai-Borwein method for compressed sensing

In this paper, we present a new nonmonotone projected BB (Barzilai-Borwein) method for solving l₁ regularization problem in compressed sensing. By exploiting the idea of determining the search stepsize in monotone projected BB algorithm (MPBB) of nonnegative matrix factorization, a direct calculation method of search stepsize which doesn't need line search and satisfies nonmonotonicity is provided. Finally, the proposed algorithm is theoretically proved to be globally convergent. Numerical experiment results demonstrate that the proposed algorithm is effective and outruns the GPSR and SpaRSA as the sparseness degrees range.